Transition of phase response properties and singularity in the circadian limit cycle of cultured cells

Input integration by the circadian clock exhibits nonadditivity and fold-change detection

Circadian clocks are synchronized by external timing cues to align with one another and the environment. Various signaling pathways have been shown to independently reset the phase of the clock. However, in the body, circadian clocks are exposed to a multitude of potential timing cues with complex temporal dynamics, raising the question of how clocks integrate information in response to multiple signals. To investigate different modes of signal integration by the circadian clock, we used Circa-SCOPE, a method we recently developed for high-throughput phase resetting analysis. We found that simultaneous exposure to different combinations of known pharmacological resetting agents elicits a diverse range of responses. Often, the response was nonadditive and could not be readily predicted by the response to the individual signals. For instance, we observed that dexamethasone is dominant over other tested inputs. In the case of signals administered sequentially, the background levels of a signal attenuated subsequent resetting by the same signal, but not by signals acting through a different pathway. This led us to examine whether the circadian clock is sensitive to relative rather than absolute levels of the signal. Importantly, our analysis revealed the involvement of a signal-specific fold-change detection mechanism in the clock response. This mechanism likely stems from properties of the signaling pathway that are upstream to the clock. Overall, our findings elucidate modes of input integration by the circadian clock, with potential relevance to clock resetting under both physiological and pathological conditions.

Cryptochrome 1 as a state variable of the circadian clockwork of the suprachiasmatic nucleus: Evidence from translational switching

The suprachiasmatic nucleus (SCN) of the hypothalamus is the principal clock driving circadian rhythms of physiology and behavior that adapt mammals to environmental cycles. Disruption of SCN-dependent rhythms compromises health, and so understanding SCN time keeping will inform management of diseases associated with modern lifestyles. SCN time keeping is a self-sustaining transcriptional/translational delayed feedback loop (TTFL), whereby negative regulators inhibit their own transcription. Formally, the SCN clock is viewed as a limit-cycle oscillator, the simplest being a trajectory of successive phases that progresses through two-dimensional space defined by two state variables mapped along their respective axes. The TTFL motif is readily compatible with limit-cycle models, and in Neurospora and Drosophila the negative regulators Frequency (FRQ) and Period (Per) have been identified as state variables of their respective TTFLs. The identity of state variables of the SCN oscillator is, however, less clear. Experimental identification of state variables requires reversible and temporally specific control over their abundance. Translational switching (ts) provides this, the expression of a protein of interest relying on the provision of a noncanonical amino acid. We show that the negative regulator Cryptochrome 1 (CRY1) fulfills criteria defining a state variable: ts-CRY1 dose-dependently and reversibly suppresses the baseline, amplitude, and period of SCN rhythms, and its acute withdrawal releases the TTFL to oscillate from a defined phase. Its effect also depends on its temporal pattern of expression, although constitutive ts-CRY1 sustained (albeit less stable) oscillations. We conclude that CRY1 has properties of a state variable, but may operate among several state variables within a multidimensional limit cycle.

Circa-SCOPE: high-throughput live single-cell imaging method for analysis of circadian clock resetting

Circadian clocks are self-sustained and cell-autonomous oscillators. They respond to various extracellular cues depending on the time-of-day and the signal intensity. Phase Transition Curves (PTCs) are instrumental in uncovering the full repertoire of responses to a given signal. However, the current methodologies for reconstructing PTCs are low-throughput, laborious, and resource- and time-consuming. We report here the development of an efficient and high throughput assay, dubbed Circadian Single-Cell Oscillators PTC Extraction (Circa-SCOPE) for generating high-resolution PTCs. This methodology relies on continuous monitoring of single-cell oscillations to reconstruct a full PTC from a single culture, upon a one-time intervention. Using Circa-SCOPE, we characterize the effects of various pharmacological and blood-borne resetting cues, at high temporal resolution and a wide concentration range. Thus, Circa-SCOPE is a powerful tool for comprehensive analysis and screening for circadian clocks' resetting cues, and can be valuable for basic as well as translational research.

A saturated reaction in repressor synthesis creates a daytime dead zone in circadian clocks

Negative feedback loops (NFLs) for circadian clocks include light-responsive reactions that allow the clocks to shift their phase depending on the timing of light signals. Phase response curves (PRCs) for light signals in various organisms include a time interval called a dead zone where light signals cause no phase shift during daytime. Although the importance of the dead zone for robust light entrainment is known, how the dead zone arises from the biochemical reactions in an NFL underlying circadian gene expression rhythms remains unclear. In addition, the observation that the light-responsive reactions in the NFL vary between organisms raises the question as to whether the mechanism for dead zone formation is common or distinct between different organisms. Here we reveal by mathematical modeling that the saturation of a biochemical reaction in repressor synthesis in an NFL is a common mechanism of daytime dead zone generation. If light signals increase the degradation of a repressor protein, as in Drosophila, the saturation of repressor mRNA transcription nullifies the effect of light signals, generating a dead zone. In contrast, if light signals induce the transcription of repressor mRNA, as in mammals, the saturation of repressor translation can generate a dead zone by cancelling the influence of excess amount of mRNA induced by light signals. Each of these saturated reactions is located next to the light-responsive reaction in the NFL, suggesting a design principle for daytime dead zone generation.

Light-entrainable circadian clocks form behavioral and physiological rhythms in organisms. The light-entrainment properties of these clocks have been studied by measuring phase shifts caused by light pulses administered at different times. The phase response curves of various organisms include a time window called the dead zone where the phase of the clock does not respond to light pulses. However, the mechanism underlying the dead zone generation remains unclear. We show that the saturation of biochemical reactions in feedback loops for circadian oscillations generates a dead zone. The proposed mechanism is generic, as it functions in different models of the circadian clocks and biochemical oscillators. Our analysis indicates that light-entrainment properties are determined by biochemical reactions at the single-cell level.

Partial synchronization of relaxation oscillators with repulsive coupling in autocatalytic integrate-and-fire model and electrochemical experiments

Experiments and supporting theoretical analysis are presented to describe the synchronization patterns that can be observed with a population of globally coupled electrochemical oscillators close to a homoclinic, saddle-loop bifurcation, where the coupling is repulsive in the electrode potential. While attractive coupling generates phase clusters and desynchronized states, repulsive coupling results in synchronized oscillations. The experiments are interpreted with a phenomenological model that captures the waveform of the oscillations (exponential increase) followed by a refractory period. The globally coupled autocatalytic integrate-and-fire model predicts the development of partially synchronized states that occur through attracting heteroclinic cycles between out-of-phase two-cluster states. Similar behavior can be expected in many other systems where the oscillations occur close to a saddle-loop bifurcation, e.g., with Morris-Lecar neurons.